32-2x^16 eching

$$32 - 2 x ^ { 16 }$$

Omil

$$2\left(x^{4}-2\right)\left(x^{4}+2\right)\left(-x^{8}-4\right)$$

Yechim qadamlari

2 omili.

$$2\left(16-x^{16}\right)$$

Hisoblang: 16-x^{16}. 16-x^{16} ni 4^{2}-\left(-x^{8}\right)^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(4+x^{8}\right)\left(4-x^{8}\right)$$

Shartlarni qayta saralash.

$$\left(x^{8}+4\right)\left(-x^{8}+4\right)$$

Hisoblang: -x^{8}+4. -x^{8}+4 ni 2^{2}-\left(-x^{4}\right)^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2+x^{4}\right)\left(2-x^{4}\right)$$

Shartlarni qayta saralash.

$$\left(x^{4}+2\right)\left(-x^{4}+2\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing. Quyidagi koʻphadlar faktorlanmagan, ularda hech qanday ratsional ildizlar topilmadi: -x^{4}+2,x^{4}+2,x^{8}+4.

$$2\left(x^{8}+4\right)\left(x^{4}+2\right)\left(-x^{4}+2\right)$$

Baholash

$$32-2x^{16}$$